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Topic: Coordinate transformations

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	Coordinate Systems
		In a coordinate system, many differences are permitted to vary at the same time ('co' having a root meaning along the lines of 'with', and 'ordinate' implying something to do with placement or measurement in some sort of scale.) The incremental change that a coordinate system records are the units of measure.
		When transforming coordinate systems it is important to think about transformation the way we think about other associative functions in information systems -- that is we are trying to define a function that simulates the actual distortion of the geometry in the unknown system.
		Ptojection Transformation: The second type of problem in reconciling coordinate systems in datasets is whre we have two coordinate systems which are different, but where the differences among them is mathematically understood from the beginning.
	www.geog.ubc.ca /courses/klink/g470/notes/coordinates/coordinates.html (2585 words)

	Coordinate Systems, Transformations and Units
		The 'transform' and 'viewBox' attributes transform user space coordinates and lengths on sibling attributes on the given element (see effect of the 'transform' attribute on sibling attributes and effect of the 'viewBox' attribute on sibling attributes) and all of its descendants.
		The result of this transformation is that the coordinate (30,30) in the new user coordinate system gets mapped to coordinate (80,80) in the original coordinate system (i.e., the coordinates have been translated by 50 units in X and 50 units in Y).
		Then, coordinate (0,0) in the new user coordinate system is mapped to the (minx,miny) corner of the tight bounding box within the user coordinate system of the applicable element and coordinate (1,1) in the new user coordinate system is mapped to the (maxx,maxy) corner of the tight bounding box of the applicable element.
	www.w3.org /TR/SVGMobile12/coords.html (6018 words)

	Coordinate Spaces and Transformations (Site not responding. Last check: 2007-09-07)
		A coordinate space is a planar space that locates two-dimensional objects by using two reference axes that are perpendicular to each other.
		A transformation is an algorithm that alters ("transforms") the size, orientation, and shape of objects.
		Transformations also transfer a graphics object from one coordinate space to another.
	msdn.microsoft.com /library/en-us/gdi/cordspac_784z.asp?frame=true (98 words)

	Background: Coordinate systems and transformations
		For the definition of a coordinate system in threedimensional space, one has only to specify the direction of one of the axes, and the orientation of one of the other axes in the plane perpendicular to this direction.
		The Geographic coordinates of the dipole axis derived from the International Geomagnetic Reference Field 1995 (IGRF-1995) are 79.30°N and 288.59°E for 1995.
		In Solar Magnetic Coordinates (SM) the Z-axis is chosen parallel to the north magnetic pole and the Y-axis perpendicular to the Earth-Sun line towards dusk.
	www.spenvis.oma.be /spenvis/help/background/coortran/coortran.html (1943 words)

	Geographic Coordinate System Transformations
		The transformations may be most readily achieved by first expressing the observed or source geographical coordinates in terms of three dimensional XYZ cartesian values (geocentric coordinates) instead of the normal angular expressions of latitude and longitude.
		Because the coordinate differences are small and the coordinates in the source and target systems are very similar in magnitude, in reversible polynomial transformations it is possible to adopt the same coordinate values for the evaluation point in both source and target systems.
		Transformations between two coordinate systems where in either system either the scale along axes differ or the axes are not orthogonal should be defined as a general affine transformation in either the parametric or geometric form.
	www.posc.org /Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs35.html (5780 words)

	Coordinate Systems, Transformations and Units - SVG 1.1 - 20030114
		Both coordinates systems are established such that the origin matches the origin of the viewport (for the root viewport, the viewport origin is at the top/left corner), and one unit in the initial coordinate system equals one "pixel" in the viewport.
		When a coordinate or length value is a number without a unit identifier (e.g., "25"), then the given coordinate or length is assumed to be in user units (i.e., a value in the current user coordinate system).
		Indicates that the user coordinate system for the contents of the 'mask' element are established using the bounding box of the element to which the mask is applied.
	www.w3.org /TR/SVG/coords.html (7070 words)

	Coordinate Systems, Transformations and Units
		The origin of both coordinate systems is at the origin of the viewport, and one unit in the initial coordinate system equals one "pixel" (i.e., a px unit as defined in [CSS2 lengths]) in the viewport.
		Unlike the transform attribute (see effect of the transform on sibling attributes), the automatic transformation that is created due to a viewBox does not affect the x, y, width and height attributes (or in the case of the 'marker' element, the markerWidth and markerHeight attributes) on the element with the viewBox attribute.
		Thus, in the the initial coordinate system, because the user coordinate system aligns exactly with the parent's coordinate system, and because often the parent's coordinate system aligns with the device pixel grid, "5px" might actually map to 5 devices pixels.
	www.schumacher-netz.de /TR/2001/SVG/PR/coords.html (6840 words)

	ASC Coordinate Transformation-The Pixlib Library
		The line arrows connecting a pair of coordinate systems indicate the coordinate transformation is both forward and backward, and the aim of the transformation is explained at the side.
		For instance, transformation of CPC to LSI is to account for chip orientation in space, and N to FP is to convert the 3-D HRMA nodal position to the 2-D pixel focal plane coordinates.
		The requested coordinate transformation from A to B is thus completed by a matrix-vector multiple performance.
	www.adass.org /adass/proceedings/adass96/heh.html (1223 words)

	Coordinate Transformations in Object Recognition (Site not responding. Last check: 2007-09-07)
		Recognition is achieved by transforming a generic perceptual coordinate system that defines the correspondence between positions specified in memory and positions in the current visual field so that memory and input representations are aligned.
		Coordinate transformations seem to underlie both object recognition and visuomotor control, and may be regarded as a general processing principle of the visual cortex.
		TMR discriminates between compensation processes in object recognition and mental imagery; coordinate transformations in recognition are more closely related to visuomotor control than to mental rotation.
	www.kyb.tuebingen.mpg.de /publication.html?publ=2284 (249 words)

	Coordinate system - Wikipedia, the free encyclopedia
		Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
		Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in the plane by an angle and a distance from the origin.
		Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates.
	en.wikipedia.org /wiki/Coordinate (756 words)

	Coordinates (mathematics) - Wikipedia, the free encyclopedia
		The coordinates of a point are the components of a tuple of numbers used to represent the location of the point in the plane or space.
		The polar coordinate systems are coordinate systems in which a point is identified by a distance from some fixed feature in space and one or more subtended angles.
		The circular coordinate system, commonly referred to as the polar coordinate system, is a two-dimensional polar coordinate system, defined by an origin, O, and a semi-infinite line L leading from this point.
	en.wikipedia.org /wiki/Coordinates_(elementary_mathematics) (847 words)

	Compound Coordinate Transformations
		There are many cases where a coordinate transformation can be more efficiently described and executed as two or more simple transformations.
		Thus, a transformation from ETRS89 to WGS 84 would be given as a pair of transformations: ETRS89 to WGS 72, followed by WGS 72 to WGS 84.
		This is the method used to define the coordinate transformation.
	www.posc.org /technical/up223/comcord.html (892 words)

	Proper Time [Internet Encyclopedia of Philosophy]
		Coordinate transformations: First is the notion of taking the description of a given process (such as a trajectory), described in one coordinate system, and transforming to its description in an alternative coordinate system.
		Now instead of transforming the processes involved, we can do the inverse, and make a transformation of the coordinate system, so that we end up with a new coordinate description of the original process, which looks exactly the same as the description of the transformed process in the original coordinate system.
		Physicists tend to regard coordinate transformations and valid object transformations interchangeably and somewhat ambiguously, and the distinction between the two is often blurred in applied physics.
	www.utm.edu /research/iep/ancillaries/Proper-Time.htm (9520 words)

	Help: Coordinate transformations (Site not responding. Last check: 2007-09-07)
		This tool is intended as a visual aid to interpret the relationships between the various coordinate systems used in space physics.
		The tool transforms the coordinates of a point in space into coordinates in a number of often used coordinate systems.
		For the calculation of the magnetic coordinates, the UNIRAD library is used with DGRF/IGRF as internal magnetic field for the specified date, and no external field.
	www.spenvis.oma.be /spenvis/help/models/coortrans.html (231 words)

	Geophysical Coordinate Transformations
		The common coordinate systems in use in solar-terrestrial relationships are described and then the transformation matrices required to convert vectors in one system to another are derived.
		In geographic coordinates, the dipole is at 11.435
		We note that this transformation usually is particularly straight forward from geographic coordinates because the geographic latitude and longitude of a point of observation is often known and the dipole is fixed in geographic coordinates.
	www-ssc.igpp.ucla.edu /personnel/russell/papers/gct1.html (4587 words)

	Plane Stress and Coordinate Transformations
		The coordinate directions chosen to analyze a structure are usually based on the shape of the structure.
		For example, the failure plane of a brittle shaft under torsion is often at a 45° angle with respect to the shaft's axis.
		The transformation of stresses with respect to the {x,y,z} coordinates to the stresses with respect to {x',y',z'} is performed via the equations,
	www.efunda.com /formulae/solid_mechanics/mat_mechanics/plane_stress.cfm (240 words)

	Change of Basis and Coordinate Transformations (Site not responding. Last check: 2007-09-07)
		The goal of this section of the lab is to talk about linear changes of coordinates, that is, switching from one basis of a vector space to a different basis.
		Given coordinates of a point in one basis, we will be able to obtain the coordinates of that point in another basis by applying the change of coordinates matrix to it.
		In this case, the green cactus is the origin of your coordinate system, "south" and "west" are your axes, and (3, 5) are your coordinates in these axes.
	math.ucsd.edu /~math20f/Fall/Lab6F/Lab6F.html (1774 words)

	Interoperable Coordinate Transformation and Identification of Coordinate Systems
		The working group developed a Unified Modeling Language object model of coordinate systems and coordinate transformations in coordination with ISO/TC211; OGC accepted interface specifications drafted using this model.
		Attributes in CS_Info are from ISO/TC211 Spatial Referencing by Coordinates.
		Commercialization of the coordinate transformation interface will probably be limited until the release of an HTTP interface.
	www.ncgia.ucsb.edu /globalgrids-book/specht (1937 words)

	Coordinate Systems, Transformations and Units - SVG 1.0 - 20010904
		The initial clipping path for the SVG document fragment is established according to the rules described in The initial clipping path.
		By establishing a new viewport, you also implicitly establish a new viewport coordinate system, a new user coordinate system, and, potentially, a new clipping path (see the definition of the 'overflow' property).
		Indicates that the attributes which specify the gradient vector (x1, y1, x2, y2) represent fractions or percentages of the bounding box of the element to which the gradient is applied.
	www.dcs.ed.ac.uk /teaching/cs2/prac8/samples/SVG/coords.html (6878 words)

	Cover Pages: Open GIS Consortium Publishes Data Model for Coordinate Reference Systems and Coordinate Transformations.
		This OGC standard data model for coordinate reference systems and coordinate transformation definition data is intended for initial use with OGC's OpenGIS Geography Markup Language (GML) and Coordinate Transformation (CT) Implementation Specifications.
		This OGC standard data model for CRS and CT definition data is intended for initial use by the Geography Markup Language (GML) and in Coordinate Transformation (CT) Implementation Specifications.
		Coordinate Conversion and Coordinate Transformation, this document, although implementing these concepts materially, refers to both collectively as 'Coordinate Transformation', thereby not using the term 'Coordinate Operation'.
	xml.coverpages.org /ni2001-08-22-a.html (722 words)

	ASTRO JAVA
		Also available on this panel is the option to adjust an objects coordinates, taking into effect the refractive index of the Earth's atmosphere.
		The Object Selection Panel enables the user to enter an object's positional data in the Equatorial coordinate system, or alternately to select from one of many pre-programmed objects, such as the sun, moon and planets, the brightest stars, and several 'deep-sky' objects.
		Other functions activated from this panel include the ability to account for the precession of the equinoxes to adjust coordinates to a specified epoch, and to calculate the approximate rising and setting times of an object.
	www.roman-britain.org /astronomy/astro.htm (334 words)

	Transformations in Coordinate Geometry - Dilations (Site not responding. Last check: 2007-09-07)
		is a transformation that produces an image that is the
		Most dilations in coordinate geometry use the origin (0,0) as the center of the dilation.
		PROBLEM: Draw the dilation image of triangle ABC with the center of dilation at the origin and a scale factor of 2.
	regentsprep.org /Regents/math/codilate/Ldilate.htm (272 words)

	Transformations in Coordinate Geometry - Translations (Site not responding. Last check: 2007-09-07)
		Let's examine some translations related to coordinate geometry.
		(This is read: "the x and y coordinates will become x-7 and y-3".
		Notice that movement left and down is negative, while movement right and up is positive - just as it is on coordinate axes.)
	regentsprep.org /Regents/math/cotran/trans.htm (123 words)

	The Java Boutique: Articles : Java 2D - A Tutorial
		This is very convenient: it is often much easier to move the coordinate system than to calculate new coordinates for each of your points.
		Shear means to stretch unevenly: an x shear moves points to the right based on how far they are from the y axis; a y shear moves points down based on how far they are from the x axis.
		This tutorial was prepared by Marty Hall for work in the Research and Technology Development Center of the Johns Hopkins University Applied Physics Lab, for courses in the Johns Hopkins Part-Time MS Program in Computer Science, and for various industry seminars and courses.
	javaboutique.internet.com /tutorials/Java2D/page07.html (733 words)

	Coordinate Systems (Site not responding. Last check: 2007-09-07)
		The ISTP Project provides a Fortran library for conversion between these coordinate systems.
		A good description of how to make transformations between the different coordinate systems can be found in a paper by M. Hapgood, "Space physics coordinate transformations: A user guide", in Planetary and Space Science, Vol.
		Geocentric inertial reference frame using the Julian Epoch of Jan. 1, 2000.
	www.srl.caltech.edu /ACE/ASC/coordinate_systems.html (161 words)

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